Semilocal momentum-space regularized chiral two-nucleon potentials up to fifth order

Abstract

We introduce new semilocal two-nucleon potentials up to fifth order in the chiral expansion. We employ a simple regularization approach for the pion-exchange contributions which (i) maintains the long-range part of the interaction, (ii) is implemented in momentum space and (iii) can be straightforwardly applied to regularize many-body forces and current operators. We discuss in detail the two-nucleon contact interactions at fourth order and demonstrate that three terms out of fifteen used in previous calculations can be eliminated via suitably chosen unitary transformations. The removal of the redundant contact terms results in a drastic simplification of the fits to scattering data and leads to interactions which are much softer (i.e. more perturbative) than our recent semilocal coordinate-space regularized potentials. Using the pion-nucleon low-energy constants from matching pion-nucleon Roy-Steiner equations to chiral perturbation theory, we perform a comprehensive analysis of nucleon-nucleon scattering and the deuteron properties up to fifth chiral order and study the impact of the leading F-wave two-nucleon contact interactions which appear at sixth order. The resulting chiral potentials lead to an outstanding description of the proton-proton and neutron-proton scattering data from the self-consistent Granada-2013 database below the pion production threshold, which is significantly better than for any other chiral potential. For the first time, the chiral potentials match in precision and even outperform the available high-precision phenomenological potentials, while the number of adjustable parameters is, at the same time, reduced by about ∼ 40%. Last but not least, we perform a detailed error analysis and, in particular, quantify for the first time the statistical uncertainties of the fourth-and the considered sixth-order contact interactions.

Atomic Nuclei From Quantum Monte Carlo Calculations With Chiral EFT Interactions

“…Within χEFT, many studies have been carried out dealing with the construction and optimization of NN and 3N interactions [60,61,62,63,64,65,66,67,68,69,70,35,50,43,71,72,73,74,75,45,76,77,78,79,59,80,81,82,83] and accompanying isospin-symmetry-breaking corrections [84,85,86]. These interactions are typically formulated in momentum space, and include cutoff functions to regularize their behavior at large momenta.…”

Benchmark calculations of pure neutron matter with realistic nucleon-nucleon interactions

“…where V is the bare NN interaction, the quantity ω is the so called starting energy. In the present work we consider spin unpolarized neutron matter, thus in equation (5) and in the following equations we drop the spin indices to simplify the mathematical notation. The Pauli operator | k a , k b Q k a , k b | projects on intermediate scattering states in which the momenta k a and k b of the two interacting neutrons are above their Fermi momentum k F since single particle states with momenta smaller that this value are occupied by the neutrons of the nuclear medium.…”

“…Over the past twenty years, establishing this basic model of nuclear physics has undergone substantial progress, driven by two major factors. First, since the advent of chiral effective field theory (χEFT), originally proposed by Weinberg in the early 1990's [1,2], we can now systematically develop nuclear many-body interactions [3][4][5][6] and consistent electroweak currents [7][8][9][10][11][12][13] that are rooted in the fundamental symmetries exhibited by the underlying theory of Quantum Chromodynamics. Second, present computational resources allow to employ these interactions and current in sophisticated many-body methods to compute a variety of nuclear systems with controlled approximations [14][15][16][17][18][19][20].…”

Local Nucleon-Nucleon and Three-Nucleon Interactions Within Chiral Effective Field Theory

“…Recently, accurate and precise chiral EFT potentials up to fifth order in the chiral expansion, i.e. N 4 LO, have been developed [73,74,75,76], and provide an extremely accurate description of NN data bases up to laboratory energies of 300 MeV with a χ 2 per datum close to one. These databases have been provided by the Nijmegen group [29,26], the VPI/GWU group [79], and more recently the Granada group [80,81,82].…”